COLLEGE OF BUSINESS VICTORIA UNIVERSITY SEMESTER 2, 2017, AABC, LIAONING CHINA
BEO2255 APPLIED STATISTICS FOR BUSINESS
Assignment 3 15 marks
Due in Week 12
Part a
A researcher is interested in quantifying the relationship between the salary of member of Board in a company and other factors such as the size of the Board (including Executives and Nonexecutives), the number of committees that the Board members are involved, Type of industry, and the success of the company. To this end, he has compiled an Excel file (Data 3A_Assignment 3_S2 2017.xls) that contains 80 members of boards from public companies listed on ASX. The variables included are as follows:
SALARY EXECUTIVES NONEXECUTIVES COMMITTEE TYPE
SUCCESS
Salary in $A
Number of EXECUTIVE board members
Number of NON-EXECUTIVE board members
Number of COMMITTEEs that board member is involved
TYPE of industry (1= Energy, 2 = Manufacturing, 3 = Financial Services, 4 = Information Technology, 5 = Utilities)
Rating of the SUCCESS (1= the worst, 5=the best)
Note that TYPE and SUCCESS are two categorical variables and four dummy variables for each of these categorical variables are included in the data file. TYPE 1 and SUCCESS 1 are considered as the base level.
Use SPSS to conduct the regression analysis and interpret SPSS outputs. In interpreting the outputs answer the following questions.
(1) Using Ordinary Least Square (OLS) method estimate the regression model. The below is the estimating model to help with model estimation (hint: use the estimated coefficients to write the regression equation based on the following model).
SALARY = β0 + β1 EXECUTIVES + β2 NONEXECUTIVES + β3 COMMITTES + β4 T2 + β5 T3+β6T4+β7T5+β8S2+β9S3+β10S4+β11S5+ε
- (2) What are the a priori signs of the coefficients based on your experience or theories and are they the same as the signs of the estimated coefficients from the model in the SPSS output?
- (3) Interpret the estimated coefficients of the model and check whether these coefficients are significant.
- (4) Use the adjusted R2 and CV to evaluate the goodness of fit of the model and using ANOVA statistics check whether the model is significant.
- (5) You have been asked to predict the SALARY of a board member in a company with 3 Executives, 2 Non-executives, 3 Committees, Industry Type of 3, and a Success of 4.
- (6) Is there any evidence that the regression might have problems associated with multi- collinearity, heteroskedasticity or non-normality of the regression residuals?
Part b
A large number of decisions involved in the consumer lending business makes it necessary to rely on models that are designed based on personal characteristics including marital status, age, income and other factors. The file Data 3B_Assignment3_S2 2017.xls has been compiled with 160 observations from a random sample of borrowers who are in full-time or part-time employment.
The bank of Victoria lending manager wants to develop a credit risk model that distinguishes between populations of good and bad borrowers. Good borrower pays principal and interest on time.
The survey that used to compile the data file dealt with whether respondents are good or bad borrowers and their attitudes towards the bank loan. The following variables are included:
Borrower Age Income Marital Profession Gender
1 if the borrower is a good borrower, 0 otherwise Age in years
Borrower’s annual earnings in $K
1 if person is married, 0 otherwise
1 if the borrower is in full-time employment, 0 otherwise 1=male,0=female
Borrowers are also asked their responses to six statements concerning the loan. The statements and the variable names are:
Cheaper
Mode Useful Informative
Payment Current
“It is cheaper to borrow from the bank of Victoria than to borrow from the other
banks.”
“I am willing to apply for online borrowing mode if available.”
“Online applications are useful to people who surf the Internet frequently.”
“I gain a lot of information from reading the PDS (Product Disclosure Statement) of the loan.”
“I borrow from the bank that charges application fee of not more than $100.” “Consumer loan helps me to keep my daily life continues.”
The responses to the attitudinal questions are coded as follows:
1 = strongly disagree 2 = disagree
3 = no view either way 4 = agree
5 = strongly agree
Use SPSS to perform a discriminant analysis in which the dependent variable is BORROWER and the independent variables are AGE, INCOME, MARITAL, PROFESSION, and GENDER.
(7) Hold out the last 50 observations from the analysis.
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- (8) Generate means, univariate ANOVAs, unstandardised function coefficients, within-groups correlations and a summary table.
- (9) Estimate the discriminant function and analyse all tables in your report.
- (10) Using the discriminant function, determine whether A person with the following characteristics is likely to be a good borrower or otherwise:
A 42 years old, male, in full-time employment and earns an annual income of $75,000.
Part c
Use SPSS to perform a factor analysis of the six attitudinal variables and analyse all tables in your report.
- (11) Produce univariate descriptive statistics and correlation coefficients.
- (12) Use principal components to extract the factors and varimax to rotate the factors. Also produce a scree plot and identify the factors.
- (13) Save the factors and use them in a discriminant analysis together with the independent variables AGE, INCOME, MARITAL, PROFESSION, and SEX.
- (14) Does using the factors improve the discriminant analysis?
Presentation guidelines
- You are required to write the report to suit the academic standards.
- Attached an assignment declaration.
- All tables and figures should contain a title that clearly explains the content.
- SPSS tables, once copied to word file, should be formatted to suite the presentation of
report.
- Interpretations should be precise and you are required to use the plain language.
- Assignments without interpretations will attract low marks.
- You are required to submit the electronic version to the VUC Dropbox and handover the
hard copy to the tutor for marking.
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